Conceptual and Practical Examination of Several Edge Detection Strategies

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Conceptual and Practical Examination of Several Edge Detection
Strategies
Shalini1, Dr. N K Singh2, Rahila Khan3
1Assistant Professor, Dept. of CSE, ITM, GIDA Gorakhpur, U.P., India
2 Professor, Dept. of CSE, ITM, GIDA Gorakhpur, U.P., India
3Assistant Professor, Dept. of CSE, KIOT, Kanpur, U.P., India
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1. INTRODUCTION
In the field of Computer Vision and Digital Image
Processing, an image needs to be analyzed to identify the
various objects present in the scene [2]. This can be done
by segmenting the entire image into its constituent using
image segmentation. Image Segmentation is the process of
partitioning a digital image into multiple regions or sets of
pixels [1] [3] [18]. Actually, partitions are different objects
in image which have the same texture or color. The result
of image segmentation is a set of regions that collectively
cover the entire image, or a set of contours extracted from
the image. All of the pixels in a region are similar with
respect to some characteristic or computed property, such
as color, intensity, or texture. Adjacent regions are
International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 10 Issue: 11 | Nov 2023. www.irjet.net p-ISSN: 2395-0072
Abstract — Image segmentation is a method of
segregating the image from the background and performs
its content comprehension. This can be done by detecting the
edges present in the scene. Edge detection is thus a vital step
of identifying and locating sharp discontinuities in an image.
Vast research has been done on various Edge detection
techniques to significantly reduce the amount of data to be
processed, filtering out useless information, while preserving
the important structural properties in an image. This
however leads to a lot of challenges in real world such as
changes in lightening conditions, dynamic background,
noise, missing existing edges, false or dislocated edge
detection. The proposed paper would present a complete
survey of different edge detection techniques that are
available. Depending upon the different performance
criterion, it would also offer idea for selecting the
appropriate tactic for edge detection. Applying the most
used experiential methods such as Sobel, Prewitt, Roberts,
Canny, Laplacian of Gaussian (LoG), in this paper we would
provide with a comparative assay on variegated edge
detection tactics. A complete tabulation of the different
segmentation techniques analyzed would also be presented
at the end of the paper.
Keywords—Image Segmentation, Edge, Edge Detection,
MATLAB
The paper is organized as follows. Section 1 is for the
purpose of providing some information about edge
detection for Image Segmentation. Section 2 is focused on
showing general approach for edge detection and focused
on classifying it two broad categories. Section 3 presents
the study and analysis of various edge detection
techniques. In section 4 the visual comparisons of various
edge detection techniques have been done by developing
software in MATLAB 7.0. In Section 5 the advantages and
significantly different with respect to the same
characteristics. The boundaries of object surfaces in a
scene often lead to oriented localized abrupt and sharp
changes in intensity of an image, called edges. Thus, Edge
is a boundary between two homogeneous regions. Edges
characterize boundaries and are therefore a problem of
fundamental importance in image processing. Edge
detection refers to the process of identifying and locating
such edges in an image. Image Edge detection significantly
reduces the amount of data and filters out useless
information, while preserving the important structural
properties in an image. The Classical methods of edge
detection involve smoothing differentiation of the image
[2]. Smoothing results in loss of information and
differentiation is an ill-conditioned problem. So it becomes
difficult to design a general edge detection algorithm
which performs well in all contexts and captures the
requirements of subsequent processing stages.
Consequently in the history of digital image processing, a
variety of edge detectors have been devised which differ in
their mathematical and algorithmic properties. This
observation combined with a commonly held belief that
edge detection is the first step in image segmentation, has
fueled a long search for a good edge detection algorithm to
use in image processing, thus leading to a steady stream of
edge detection algorithms published in the image
processing journals over the last three decades [13]. Since
edge detection is a principal area of research in image
processing for object detection, it is crucial to have a good
understanding of edge detection algorithms. This paper is
an account of some widely used approaches to detect
edges for segmentation.
disadvantages of various edge detection techniques are
discussed. Section 6 provides with the conclusion reached
by analysis and visual comparison.

2. EDGE DETECTION TECHNIQUE
2.1 Description
The generic method of edge detection involves
convolving the image with an operator (a 2-D filter), which
is constructed to be sensitive to large gradients in the
image while returning values of zero in invariable regions.
Large number of edge detection operators is available; each
designed to be sensitive to certain edge type. While
choosing a particular edge detection operator, variables
that need to be considered include Edge orientation, Noise
environment and Edge structure. The operator once
selected then needs to be operated on the image to detect
point that might lie in an edge. Such points are known as
the edge points.
An extensive collection of objectives should be
defined for the computation of edge points. The success of
the approach used depends on the comprehensiveness of
the objectives. These objectives must be decisive enough to
demarcate the desired behavior of the detector while
making as minimal assumptions as possible about the
possible form of the solution. Operators can be emended to
look for horizontal, vertical, or diagonal edges. The
geometry of the operator ascertains a distinct direction in
which it is most sensitive to edges. Detection and
localization criteria for a class of edges are defined, and
mathematical forms are presented for these criteria
functional on the operator impulse response. A consequent
criterion is then added to ensure that the detector has a
single response to an edge. Numerous criteria in numerical
optimization are used to derive detectors for several
prevalent image features that include step edges. Once the
analysis of step edges is complete, a natural uncertainty
between detection and localization performance is
established. Based on this establishment, a single operator
shape is designed which is optimal at any scale. This simple
detector can then be extended using operators of several
widths to cope with variegated signal-to-noise ratios in the
image. Edge detection is prohibitive in noisy images, since
both the noise and the edges comprises of high frequency
contents. One possible solution would be to reduce the
noise by smoothening. This would however result in
blurred and distorted edges. The size of operators is kept
large when applied on noisy images, so that sufficiently
large numbers of pixels are averaged to discount localized
noisy pixels. However, the detected edges in this case are
less accurately localized.
Also in real life scenes, the chances of an edge to
have a step change in intensity are very rare. The reasons
may be refraction or poor focus on object while capturing
its image. The operator needs to be chosen to be responsive
to such a gradual change in object boundaries in those
cases. Otherwise problems of false edge detection, missing
true edges, edge localization, high computational time and
problems due to noise etc might arise. Therefore,
speculative comparison of variegated edge detection
techniques is performed and the performance of the
different techniques is analyzed in different conditions.
2.2 Types
There are various ways to perform edge detection,
the majority of which may be grouped into two broad
categories:
(1) Gradient based Edge Detection:
The gradient method uses the maximum and minimum
values of the first order derivative for detecting the edges.
(2) Laplacian based Edge Detection:
The Laplacian method uses the zero crossings in second
order derivative of the image to detect edges.
Assume the intensity graph of an edge shown by the jump
in figure – 1.
Fig – 1: Intensity graph of an edge
If we calculate the gradient of the signal below
(which, in 1D, is just the first order derivative with respect
to t) we get the graph as shown in figure – 2. As clear from
the graph, maximum value is located at the center of the
edge in original signal.
Fig – 2: Intensity graph for gradient of the signal

This is the characteristic feature of gradient
method of edge detection. In this, a pixel is said to be an
edge pixel if and only if the value of its gradient is greater
than a specified threshold. As already stated, edges have
higher pixel intensity values as those surrounding it. So
once a threshold value is specified, the gradient value of the
pixel is compared to the threshold value and it is marked as
an edge pixel if the value exceeds the threshold. Moreover,
when the first derivative for a particular pixel is at a
maximum, its second order derivative is zero.
Consecutively, edge pixels in an image may be found out by
locating the zeros in second order derivative. This method
comes under the category of Laplacian and can be
graphically depicted as in figure – 3.
Fig – 3: Laplacian Method
3. EDGE DETECTION FOR IMAGE SEGMENTATION
3.1 Introduction
The edge detection techniques firstly convert
image to edge image using the abrupt changes that occur in
the intensity of the image due to edges and boundaries. An
edge image is achieved without performing any changes in
actual physical qualities of the original image [12] [16].
Objects in an image might consist of different color levels.
As already stated, an edge in an image is a significant local
change in the image intensity, usually associated with a
discontinuity in either the image intensity or the first
derivative of the image intensity. These discontinuities in
the image intensity can be either Step edge, in which the
image intensity abruptly changes from one value on one
side of the discontinuity to a different value on the opposite
side, or a Line Edges, where the image intensity abruptly
changes value but then returns to the starting value within
some short distance [3]. However, Step and Line edges are
quite rare in real images. Because of reflection effects,
limitations of image capturing device, low frequency
components or the smoothing introduced by most sensing
devices, sharp discontinuities rarely exist in real life scenes
.Thus, step edges become Ramp Edges and Line Edges are
replaced by Roof edges, where intensity changes are not
instantaneous but occur over a finite distance [15].
Exemplification of these edge shapes are shown in figure –
4.
Fig – 4: Type of Edges: (a) Step Edge (b) Ramp Edge (c)
Line Edge (d) Roof Edge
3.2 Steps in Edge Detection
Generally, the edge detection process comprises of
the three common steps namely Filtering, Enhancement
and Detection. The brief description of these steps in edge
detection is as follows:
3.2.1. Filtering
Often image is corrupted by random variations in
the intensity values of the image, which is referred to as the
noise. Some of its common types being salt and pepper,
impulse, Gaussian, uniform, erlang (gamma) noise. Filtering
is done to remove these noises from the image, however
more filtering to reduce noise results in a loss of edge
strength [17]. Hence, there is a trade-off between edge
strength and noise reduction.
3.2.2. Enhancement
This step is performed to facilitate the edge
detection process. It emphasizes those pixels where there is
a considerable change in local intensity value. It is often
done by calculating the local gradient magnitude [14].
3.2.3. Detection
There may be many points in the image having
non-zero values for gradient that do not qualify to be the
edge pixels. So some processing should be done to
determine which of such points are edge points and which
are not. Most commonly, thresholding is done to achieve
this purpose. [13]
3.3. Edge Detection Methods
There are five types of most frequently used edge
detection methods. These are (1) Robert’s Cross Edge
Detection Method, (2) Sobel Edge Detection Method, (3)
Prewitt Edge Detection Method, (4) Laplacian of Gaussian
Edge Detection Method, and (5) Canny Edge Detection
Method [18]. The details of methods as follows:

The Roberts Cross operator is simple, quick to
compute and performs fast 2-D spatial gradient
measurement on an image. Pixel values at each point in the
output 2-D intensity image represent the estimated
absolute magnitude of the spatial gradient of the input
image at that point. This operator consists of a pair of 2×2
convolution kernels which is shown in figure – 5. One
kernel can simply be obtained by rotating the other by 90°
[4].
Fig – 5: Robert’s Cross Operator Mask
These kernels are designed in such a way that is
responds maximally to the edges running at 45° to the pixel
grid, each kernel for one of the two perpendicular
orientations. The kernels can initially be applied to the
input image separately, producing separate measurements
of the gradient component in each orientation (let it be Gx
and Gy). These are then combined to calculate the absolute
magnitude of the gradient at each point and the orientation
of that gradient. The gradient magnitude is determined by
the formula:
However, most commonly an approximate magnitude is
computed using:
which is much faster to compute.
The angle of orientation of the edge (relative to the pixel
grid orientation) is determined by:
3.3.2. Sobel Operator [20]
The Sobel operator comprises of a pair of 3×3
convolution kernels as shown in figure – 6. As in case of
Robert’s Cross, in this technique also one kernel can be
obtained simply by rotating the other by 90°.
Fig – 6: Sobel Operator Mask
These kernels are designed in such a way that is
responds maximally to the edges running vertically and
horizontally relative to the pixel grid, one kernel for each of
the two perpendicular orientations. The kernels can
initially be applied to the input image separately, producing
separate measurements of the gradient component in each
orientation (let it be Gx and Gy). These are then combined
to calculate the absolute magnitude of the gradient at each
point and the orientation of that gradient. The gradient
magnitude is determined by the formula:
However, most commonly an approximate magnitude is
computed using:
which is much faster to compute.
The angle of orientation of the edge (relative to the
pixel grid orientation) is determined by:
3.3.3. Prewitt’s operator: [20]
Prewitt operator [5] works very similarly to the
Sobel operator and is used for detecting vertical and
horizontal edges present in images as shown in figure – 7.
Fig -7: Prewitt’s Operator Mask
3.3.4. Laplacian of Gaussian: [20]
3.3.1. Robert’s cross operator: [20]
The Laplacian of any image highlights the regions
of abrupt intensity change and is therefore often used for
detection of edges. The Laplacian is a 2-D isotropic measure
of the 2nd order spatial derivative of an image. To compute
the Laplacian, it is first smoothed, often using Gaussian
Smoothing Filter to reduce its sensitivity to noise, then its
2nd order derivative is computed. The Laplacian normally
takes a gray level image as input and produces another
gray level image as output. The Laplacian L(x, y) of an
image with its intensity value for each pixel I(x, y) is given
by:
As a digital image can be represented by a set of
discrete pixels, a discrete convolution kernel needs to be
devised that can approximate the second order derivatives

Fig – 8: Three commonly used discrete approximations to
the Laplacian filter.
These kernels are very sensitive to noise, as they
are approximating a second derivative measurement on the
image. So as already discussed, it must be Gaussian
Smoothed before applying the Laplacian filter.
This helps in reducing the high frequency noise
components, prior to the differentiation process. In fact,
one can design a hybrid filter by convolving the Gaussian
smoothing filter with the Laplacian filter, to achieve the
desired result. This would be advantageous in two ways:
firstly only a few arithmetic operations would be required
as both Gaussian and the Laplacian kernels are much
smaller than the image. Secondly, as the LoG (i.e., the
Laplacian of Gaussian) [6] is pre-computed so only one
convolution would be performed at run-time on the image.
The 2-D LoG function [7] with Gaussian standard
deviations, centered on zero has the following formula as
shown in figure – 9.
Fig – 9: The 2-D Laplacian of Gaussian (LoG) function. The
x and y axes are marked in standard deviations ( ).
A discrete kernel that would approximate the
above function (for a Gaussian = 1.4) is shown in figure -
10.
Fig – 10: Discrete approximation to LoG function with
Gaussian = 1.4
Note that on a discrete grid, the simple Laplacian
can be seen as a limiting case of the LoG for narrow
Gaussians [8]-[10]. This is because smoothing with a very
narrow Gaussian on a discrete grid has no effect.
3.3.4. Canny Edge Detection Algorithm [20]
The Canny Edge Detection Algorithm is a multi stage
algorithm which was designed by John F. Canny in 1986 to
detect a wide range of edges in variety of images. This
technique is also referred to as the Optimal Edge Detector
which aims at:
1. Congenial detection – able to mark as many real
edges in the image as possible.
as per the definition of the Laplacian [5]. The most common
kernels for this purpose are shown in figure – 8.
2. Congenial localization – able to mark as close as
possible to the edge in the real image.
3. Minimal response – each edge should be marked
exactly once and false edges because of noise
should not be created.
He succeeded in achieving his goal and published it in
his paper "A Computational Approach to Edge
Detection"[19] in which he combined and improved upon
the methods that were already stated at that time. The
prime consideration for that approach is striving for low
error rate. Second issue being well localized edge points.
Lastly being the single response to each edge. Based on the
above stated criterion, canny edge detector uses the
following steps:
1. The original image is filtered out before locating and
detecting any edges. This is performed using a suitable
Gaussian Smoothing Filter. The Convolution mask used
for this purpose is usually much smaller than the actual
image. So, it is rolled over the entire image,
manipulating only a square of pixels at a time. The

2. Once smoothing of image is done by eliminating the
noise using Gaussian Filter, the edge strength is to
calculate by taking its gradient. To do so, Sobel
operator is used which has been already discussed.
3. Compute the direction of the edge using the gradient in
x and y direction. Whenever the gradient in the x
direction is equal to zero, the edge direction must be
equal to 90 degrees or 0 degrees, depending on what
the value of the gradient in the y-direction is equal to. If
Gy has a value of zero, the edge direction will equal 0
degrees. Otherwise, the edge direction will equal 90
degrees. The formula for finding the edge direction is
as follows:
Theta = invtan (Gy / Gx)
4. After finding the direction of edge in previous step, that
direction is related to a standard one. To understand
this, let us consider the pixels of a 5X5 image:
0 0 0 0 0
0 0 0 0 0
0 0 1 0 0
0 0 0 0 0
It is evident that there are only four possible
directions for the pixel with value “1”: horizontal direction
(0 degrees), positive diagonal (45 degrees), vertical
direction (90 degrees), or negative diagonal (135 degrees).
Hence, the pixel in question needs to be resolved in one of
the four directions depending on which direction it is
closest to. So now the edge orientation must be resolved
into one of these four directions depending on which
direction it is closest to. This can be understood visually by
taking a semi circle and dividing it into 5 regions as shown
in figure – 11.
Fig – 11: Edge orientation
Each of the regions can be interpreted as follows:
 Horizontal Edge (0o ) for any edge falling in the purple
blue region (22.5 to 67.5 degrees)
 Vertical Edge (90o ) for any edge falling in the green
region (67.5 to 112.5 degrees)
 Negative diagonal Edge (135o ) for any edge falling in
the yellow region (112.5 to 157.5 degrees)
5. Next the non-maximum suppression is applied after
resolving the edge direction. It is done by tracing along
standard edge directions and discarding all those pixels
that do not fall in that trace, thereby giving only a thin
line as output.
6. The output image may contain streaking effect caused
by the operator output fluctuating above and below the
threshold. This is shown as breaking up of the edge
contour. So, needs to be eliminated. This is done by
using two thresholds instead of one. In a single
threshold technique, if T1 is applied to the image as the
threshold value and edge itself has the average
strength equal to T1, then there may be cases where
due to noise, the edge strength dips below or extends
above the threshold resulting in edge pixel being
discarded and thus producing a dashed line. So, to
avoid it, hysteresis method uses two threshold values:
T1 and T2. Hence any pixel which has strength as low
localization error in the detected edges increases
slightly as the Gaussian width is increased and if the
width of Gaussian mask is increased, it lowers the
detector's sensitivity to noise.
0 0 0 0 0
or red region (0 to 22.5 & 157.5 to 180 degrees)
 Positive diagonal Edge (45o ) for any edge falling in the
as the lo. To avoid this, hysteresis uses 2 thresholds, a
high and a low. Any pixel in the image that has a value
greater than T1 is presumed to be an edge pixel, and is
marked as such immediately. Then, any pixels that are
connected to this edge pixel and that have a value
greater than T2 are also selected as edge pixels. If you
think of following an edge, you need a gradient of T2 to
start but you do not stop till you hit a gradient below
T1.
4. EXPERIENTIAL ANALYSIS OF VARIOUS EDGE
DETECTION ALGORITHMS
All the above stated Edge Detection techniques have been
applied on the figure – 12 to provide the readers with
visual comparisons among all the methods.
Fig – 12: Original Image

Fig – 13: Resultant Binary Image
The resultant edge detected images are as shown below:
Fig – 14: Robert’s Cross Image
Fig – 15: Sobel Image
Fig – 16: Prewitt Image
Fig – 17: LoG Image
Fig – 18: Canny Image
As clear from the images as expected Canny provides with
the best results. This is because non maximal suppression
is used to give thin edges and hysteresis is used to avoid
streaking. The results of another image being detected are
also given to affirm the above results.
Fig – 19: Original Binary Image
Fig – 20: Robert’s Cross Image

Fig – 21: Sobel Image
Fig – 22: Prewitt Image
Fig – 23: LoG Image
Fig – 24: Canny Image
5. ADVANTAGES AND DISADVANTAGES OF EDGE
DETECTOR
OPERATOR: Classical (Robert’s Cross, Sobel,
Prewitt)
ADVANTAGES: Simple and fast.
DISADVANTAGES: Inaccurate and prone to error
due to noise.
Table – 1: Classical Operators
OPERATOR: Zero-Crossing Methods
(Laplacian, Second Order
Derivative)
ADVANTAGES: Good detection of edges and
correct orientations. Symmetric
in all edge directions.
DISADVANTAGES: Responds to only some of the
existing edges, Noise Sensitive.
Table – 2: Zero-Crossing Methods
OPERATOR: Laplacian of Gaussian (LoG)
ADVANTAGES: Good edge localization, Analyses
wider area around the edge pixel.
DISADVANTAGES: Inefficient results at the corners,
curves and where the gray level
intensity function varies. The
Laplacian filter does not find the
edge orientation.
Table – 3: Laplacian of Gaussian (LoG) Operator
As edge detection is a fundamental step in
computer vision, it is necessary to point out the true edges
to get the best results from the matching process. That is
why it is important to choose edge detectors that fit best to
the application. In this respect, we first present some
advantages and disadvantages of Edge Detection
Techniques [13]-[21] within the context of our
classification in table [1] – [4].
OPERATOR: Gaussian (Canny)
ADVANTAGES: Error rate is quite low, Good
Localization and response.
Improving signal to noise ratio.
Better results in noisy conditions.
DISADVANTAGES: Slow and Complex Computations,
False zero crossing, Time
consuming.
Table – 4: Gaussian (Canny) Operator
6. CONCLUSION
As edge detection plays a primary step in identifying
the various objects in an image, so it is very essential to
understand each of the edge detection filters. In this paper,
we studied edge detection techniques namely Gradient-
based and Laplacian based. The software used to for
performing all the edge detection techniques on a binary
image is MATLAB 2010. Gradient-based algorithms have a
major drawback that these are quite sensitive to noise. The
performance of the Canny algorithm on the other hand,
relies mainly on the changing parameters i.e., the size of

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